This means that customers who hold accounts at the bank would have to pay PNC, the 10th-largest bank in the US by assets, a fee to hold the money in the bank instead of vice versa.

And while today's interest rates may be paltry, customers can at least earn something for parking their cash at the bank.

For example, in New York City a PNC savings account with under $2,500 earns 0.01% interest monthly — 0.05% if you have a PNC checking account — according to the company's website. Standard savings accounts with over $2,500 earn 0.10% interest with a PNC checking account.

But based on Demchak's remarks, however, these fees seem likely to increase.

Earlier this month during congressional testimony, Federal Reserve Chair Janet Yellen was asked extensively about negative interest rates. She said that while the Fed was investigating the impact of such a move it was unlikely to happen anytime soon, saying, "We have work to do to judge whether they would be workable here."

And with the Fed seemingly intent on raising interest rates, a cut to negative territory is very much speculative at this point. But the market is certainly asking about it.

So while the initial market-based evidence suggests negative interest rates have been bad for the global economy, this is among the first evidence on how this move could affect regular consumers in the US.